#include #include #include template struct ModInt { using lint = long long; int val; // constructor ModInt(lint v = 0) : val(v % MOD) { if (val < 0) val += MOD; }; // unary operator ModInt operator+() const { return ModInt(val); } ModInt operator-() const { return ModInt(MOD - val); } ModInt inv() const { return this->pow(MOD - 2); } // arithmetic ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; } ModInt pow(lint n) const { auto x = ModInt(1); auto b = *this; while (n > 0) { if (n & 1) x *= b; n >>= 1; b *= b; } return x; } // compound assignment ModInt& operator+=(const ModInt& x) { if ((val += x.val) >= MOD) val -= MOD; return *this; } ModInt& operator-=(const ModInt& x) { if ((val -= x.val) < 0) val += MOD; return *this; } ModInt& operator*=(const ModInt& x) { val = lint(val) * x.val % MOD; return *this; } ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); } // compare bool operator==(const ModInt& b) const { return val == b.val; } bool operator!=(const ModInt& b) const { return val != b.val; } bool operator<(const ModInt& b) const { return val < b.val; } bool operator<=(const ModInt& b) const { return val <= b.val; } bool operator>(const ModInt& b) const { return val > b.val; } bool operator>=(const ModInt& b) const { return val >= b.val; } // I/O friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { lint v; is >> v; x = v; return is; } friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template struct Edge { int src, dst; Cost cost; Edge(int src = -1, int dst = -1, Cost cost = 1) : src(src), dst(dst), cost(cost){}; bool operator<(const Edge& e) const { return this->cost < e.cost; } bool operator>(const Edge& e) const { return this->cost > e.cost; } }; template struct Graph { std::vector>> graph; Graph(int n = 0) : graph(n) {} void span(bool direct, int src, int dst, Cost cost = 1) { graph[src].emplace_back(src, dst, cost); if (!direct) graph[dst].emplace_back(dst, src, cost); } int size() const { return graph.size(); } void clear() { graph.clear(); } void resize(int n) { graph.resize(n); } std::vector>& operator[](int v) { return graph[v]; } std::vector> operator[](int v) const { return graph[v]; } }; struct UnionFind { std::vector par, sz; int gnum; explicit UnionFind(int n) : par(n), sz(n, 1), gnum(n) { std::iota(par.begin(), par.end(), 0); } int find(int v) { return (par[v] == v) ? v : (par[v] = find(par[v])); } void unite(int u, int v) { u = find(u), v = find(v); if (u == v) return; if (sz[u] < sz[v]) std::swap(u, v); sz[u] += sz[v]; par[v] = u; --gnum; } bool same(int u, int v) { return find(u) == find(v); } bool ispar(int v) { return v == find(v); } int size(int v) { return sz[find(v)]; } }; constexpr int MOD = 1000000007; using mint = ModInt; void solve() { int n, m; mint x; std::cin >> n >> m >> x; Graph graph(n); UnionFind uf(n); while (m--) { int u, v, w; std::cin >> u >> v >> w; if (uf.same(--u, --v)) continue; uf.unite(u, v); graph.span(false, u, v, w); } mint ans = 0; auto dfs = [&](auto f, int v, int p) -> int { int sz = 1; for (auto e : graph[v]) { int u = e.dst; if (u == p) continue; int csz = f(f, u, v); ans += x.pow(e.cost) * csz * (n - csz); sz += csz; } return sz; }; dfs(dfs, 0, -1); std::cout << ans << "\n"; } int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); solve(); return 0; }